Calculation Model for the Steady-State Vibration Amplitude of a New Type of Cascaded Composite Structure-Based Ultrasonic Transducer

The steady-state vibration amplitude is an important performance indicator of high-frequency ultrasonic transducers for ultrasonically assisted manipulating, machining, and manufacturing. This work aimed to develop a calculation model for the steady-state vibration amplitude of a new type of dual-branch cascaded composite structure-based ultrasonic transducer that can be used in the packaging of microelectronic chips. First, the steady-state vibration amplitude of the piezoelectric vibrator of the transducer was derived from the piezoelectric equation. Second, the vibration transfer matrices of the tapered ultrasonic horns were obtained by combining the vibration equation, the continuous condition of the displacement, and the equilibrium condition of the force. Calculation models for the steady-state vibration amplitude of the two working ends of the transducer were then developed. A series of exciting trials were carried out to test the performance of the models. Comparison between the calculated and measured results for steady-state vibration amplitude showed that the maximum deviation was 0.0221 μm, the minimum deviation was 0.0013 μm, the average deviation was 0.0097 μm, and the standard deviation was 0.0046 μm. These values indicated good calculation accuracy, laying a good foundation for the practical application of the proposed transducer.